Electromagnetic units of measure
In physics many are unit systems for electrical and magnetic quantities have been developed. The SI has prevailed for the most part; At least in theoretical physics, however, some authors prefer the Gaussian variant of the CGS system.
Not only the specific selection, but also the number of basic quantities in a physical system of units is arbitrary: One can eliminate basic quantities from a unit system by choosing instead the proportionality factor in a linear “law of nature” as a dimensionless number. In theoretical atomic and particle physics, for example, one works with a system of units that has a single base quantity, since vacuum, the speed of light and Planck's quantum of action are set equal to 1.
Basics
Electromagnetic quantities are linked to mechanical quantities by several linear laws. The following relationships are particularly relevant for the choice of the unit system:
The Coulomb law , which gives the force F between two point charges Q _{1} and Q _{2} at a distance r ,
the Ampère force law , the force F between two currents I _{1} and I _{2} carrying conductors of the length L in the distance d indicates
 ;
and Faraday's law of induction ,
The Coulomb force exerted by static charges and the Lorentz force exerted by moving charges can be compared directly with one another; the context contains the speed of light c .
This leaves two independent proportionality constants and , which allow an arbitrary choice of an electrical and a magnetic base unit. In systems of measurement that explicitly reduce the electromagnetic quantities to mechanical quantities, one can choose both constants as dimensionless numbers or as mechanical quantities of arbitrary dimensions.
Electrostatic system of units
The Electrostatic System of Units (abbreviated esu , or ESU for e lectro s tatic u nits ) is the former way, that is ; so is .
Electromagnetic system of units
The Electromagnetic System of Units (abbreviated emu , or EMU for e lectro m agnetic u nits ) sets ; so is .
Gaussian system of units
The Gaussian system of units chooses like the electrostatic system and thus ; it then assumes that the speed of light appears in the Maxwell equations in a perfectly symmetrical form.
HeavisideLorentz unit system
The HeavisideLorentz system of units also chooses , but differs from the Gaussian system in the choice . The factor 4π anticipates an integration over the solid angle; it makes Coulomb's law more complicated, but simplifies the calculation of the capacitance of a plate capacitor.
International system of units
The International System of Units (SI) has an additional base unit, the ampere . This results in a further constant, the magnetic field constant , as well as the electrical field constant linked to it . The SI sets , and .
Before the change in the SI system of units in 2019 , the ampere was defined by the Amperes law of force . Therefore the magnetic field constant had an exact value , and since the definition of the meter is specified, it also had an exact value. With the current definition of the ampere, and are measured quantities with measurement uncertainty.
Important formulas
The following table gives an overview of the form of the most important equations in electrodynamics in the various systems of units:
theme  formula  Constant K (or , ) in the following system of units:



SI  electro statically 
electro magnetic 
Gauss  Heaviside Lorentz 

Coulomb's law 

Force effect of parallel currents 

BiotSavart law 

Lorentz force  
Dielectric polarization  ,  ,  ,  ,  ,  
magnetization  ,  ,  ,  ,  ,  
microscopic Maxwell equations 


          
,  ,  ,  ,  , 
Electromagnetic units in different systems
Electromagnetic quantity 
unit  Gaussian unit in cgs  

SI  ESU  EMU  Gauss  
charge  Q  1 C  ≙  10 ^{−1 } c  statC  10 ^{−1}  ABC  10 ^{−1 } c  Fr.  Fr = statC =  g ^{1/2} cm ^{3/2} s ^{−1} 
Amperage  I.  1 A  ≙  10 ^{−1 } c  statA  10 ^{−1}  abA  10 ^{−1 } c  statA  statA =  g ^{1/2} cm ^{3/2} s ^{−2} 
tension  U  1 V  ≙  10 ^{8 } c ^{−1}  statV  10 ^{8}  abV  10 ^{8 } c ^{−1}  statV  statV =  g ^{1/2} cm ^{1/2} s ^{−1} 
electric field strength  E.  1 V / m  ≙  10 ^{6 } c ^{−1}  statV / cm  10 ^{6}  abV / cm  10 ^{6 } c ^{−1}  statV / cm  statV / cm =  g ^{1/2} cm ^{−1/2} s ^{−1} 
electric dipole moment  p  1 C · m  ≙  10 ^{1 } c  statC · cm  10 ^{1}  abC cm  10 ^{19 } c  D.  D =  g ^{1/2} cm ^{5/2} s ^{−1} 
magnetic flux density  B.  1 T  ≙  10 ^{4 } c ^{−1}  instead of  10 ^{4}  G  10 ^{4}  G  G =  g ^{1/2} cm ^{−1/2} s ^{−1} 
magnetic field strength  H  1 A / m  ≙  4π · 10 ^{−3 } c  statA / cm  4π · 10 ^{−3}  Oe  4π · 10 ^{−3}  Oe  Oe =  g ^{1/2} cm ^{−1/2} s ^{−1} 
magnetic dipole moment  m, μ  1 A · m ^{2}  ≙  10 ^{3 } c  statA cm ^{2}  10 ^{3}  abA cm ^{2}  10 ^{3}  erg / G  G =  g ^{1/2} cm ^{5/2} s ^{−1} 
magnetic flooding  Θ  1 A  ≙  4π · 10 ^{−1 } c  statA  4π · 10 ^{−1}  abA  4π · 10 ^{−1}  Gb  Gb =  g ^{1/2} cm ^{1/2} s ^{−1} 
magnetic river  Φ  1 Wb  ≙  10 ^{8 } c ^{−1}  statT cm ^{2}  10 ^{8}  G cm ^{2}  10 ^{8}  Mx  Mx =  g ^{1/2} cm ^{3/2} s ^{−1} 
resistance  R.  1 Ω  ≙  10 ^{9 } c ^{−2}  s / cm  10 ^{9}  abΩ  10 ^{9 } c ^{−2}  s / cm  cm ^{−1} s  
specific resistance  ρ  1 Ω · m  ≙  10 ^{11 } c ^{−2}  s  10 ^{11}  abΩ cm  10 ^{11 } c ^{−2}  s  s  
capacity  C.  1 F.  ≙  10 ^{−9 } c ^{2}  cm  10 ^{−9}  abF  10 ^{−9 } c ^{2}  cm  cm  
Inductance  L.  1 H.  ≙  10 ^{9 } c ^{−2}  cm ^{−1} s ^{2}  10 ^{9}  fromH  10 ^{9 } c ^{−2}  cm ^{−1} s ^{2}  cm ^{−1} s ^{2}  
electrical power  P  1 V * A = 1 W  =  10 ^{7}  erg / s  10 ^{7}  erg / s  10 ^{7}  erg / s  erg / s =  g cm ^{2} s ^{−3} 
The "≙" symbol indicates that this is not a simple conversion of units of measure. The CGS sizes generally have a different dimension than the corresponding size in the SI . That is why it is usually not allowed to simply replace the units in formulas. c is the speed of light .
literature
 John David Jackson: Classical Electrodynamics. Appendix on Units and Dimensions (also published in German under the title Classical Electrodynamics ).
Web links
 Unit Systems in Electromagnetism  Guide from the University of Surrey
Individual evidence
 ↑ Resolution 1 of the 26th CGPM (2018), Appendix 2. In: bipm.org. Bureau International des Poids et Mesures , accessed July 3, 2020 .